13C relaxation experiments for aromatic side chains employing longitudinal- and transverse-relaxation optimized NMR spectroscopy

Aromatic side chains are prevalent in protein binding sites, perform functional roles in enzymatic catalysis, and form an integral part of the hydrophobic core of proteins. Thus, it is of great interest to probe the conformational dynamics of aromatic side chains and its response to biologically relevant events. Indeed, measurements of (13)C relaxation rates in aromatic moieties have a long history in biomolecular NMR, primarily in the context of samples without isotope enrichment that avoid complications due to the strong coupling between neighboring (13)C spins present in uniformly enriched proteins. Recently established protocols for specific (13)C labeling of aromatic side chains enable measurement of (13)C relaxation that can be analyzed in a straightforward manner. Here we present longitudinal- and transverse-relaxation optimized pulse sequences for measuring R (1), R (2), and {(1)H}-(13)C NOE in specifically (13)C-labeled aromatic side chains. The optimized R (1) and R (2) experiments offer an increase in sensitivity of up to 35 % for medium-sized proteins, and increasingly greater gains are expected with increasing molecular weight and higher static magnetic field strengths. Our results highlight the importance of controlling the magnetizations of water and aliphatic protons during the relaxation period in order to obtain accurate relaxation rate measurements and achieve full sensitivity enhancement. We further demonstrate that potential complications due to residual two-bond (13)C-(13)C scalar couplings or dipolar interactions with neighboring (1)H spins do not significantly affect the experiments. The approach presented here should serve as a valuable complement to methods developed for other types of protein side chains.     

Assessing potential bias in the determination of rotational correlation times of proteins by NMR relaxation

The various factors that influence the reliable and efficient determination of the correlation time describing molecular reorientation of proteins by NMR relaxation methods are examined. Nuclear Overhauser effects, spin-lattice, and spin-spin relaxation parameters of 15N NMR relaxation in ubiquitin have been determined at 17.6, 14.1, 11.7 and 9.4 Tesla. This unusually broad set of relaxation parameters has allowed the examination of the influence of chemical shift anisotropy, the functional form of the model-free spectral density, and the reliability of determined spin- spin relaxation parameters on the characterization of global tumbling of the protein. Treating the 15N chemical shift anisotropy (CSA) as an adjustable parameter, a consensus value of –170 ± 15ppm for the breadth of the chemical shift tensor and a global isotropic correlation time of 4.1ns are found when using the model-free spectral density to fit T1 and NOE data from all fields. The inclusion of T2 relaxation parameters in the determination of the global correlation time results in its increase to 4.6ns. This apparent inconsistency may explain a large portion of the discrepancy often found between NMR- and fluorescence-derived m values for proteins. The near identity of observed T2 and T1 values suggests that contributions from slow motions are not the origin of the apparent inconsistency with obtained T1 and NOE data. Various considerations suggest that the origin of this apparent discrepancy may reside in a contribution to the spectral density at zero frequency that is not represented by the simple model-free formalism in addition to the usual experimental difficulties associated with the measurement of these relaxation parameters. Finally, an axially symmetric diffusion tensor for ubiquitin is obtained using exclusively T1 and NOE data. A recommendation is reached on the types and combinations of relaxation data that can be used to reliably determine m values. It is also noted that the reliable determination of m values from 15N T1 and NOE relaxation parameters will become increasingly difficult as m increases.     

Transient versus steady state NOE in paramagnetic molecules Cu2Co2SOD as an example

Truncated, steady state and transient NOE experiments have been performed on bovine Cu2Co2 superoxide dismutase. The effectiveness of the different NOE experiments in the general case of paramagnetic macromolecules is discussed. It is concluded that steady state NOEs give superior results. The validity of the two spins approximation is discussed, and NOE values for a fully coupled set of nuclei have been calculated. Transient NOE experiments, when properly performed, confirm the previous assignment of the hyperfine shifted signals in Cu2Co2SOD based on steady state NOE measurements [(1989) Inorg. Chem. 28, 4650] and eliminate any further reason for controversy on an important issue as the assignment of the 1H NMR signals of protons of metal-coordinated imidazoles.     

Metropolis Monte Carlo calculations of DNA structure using internal coordinates and NMR distance restraints: An alternative method for generating a high-resolution solution structure

Summary A new method, a restrained Monte Carlo (rMC) calculation, is demonstrated for generating high-resolution structures of DNA oligonucleotides in solution from interproton distance restraints and bounds derived from complete relaxation matrix analysis of two-dimensional nuclear Overhauser effect (NOE) spectral peak intensities. As in the case of restrained molecular dynamics (rMD) refinement of structures, the experimental distance restraints and bounds are incorporated as a pseudo-energy term (or penalty function) into the mathematical expression for the molecular energy. However, the use of generalized helical parameters, rather than Cartesian coordinates, to define DNA conformation increases efficiency by decreasing by an order of magnitude the number of parameters needed to describe a conformation and by simplifying the potential energy profile. The Metropolis Monte Carlo method is employed to simulate an annealing process. The rMC method was applied to experimental 2D NOE data from the octamer duplex d(GTA-TAATG)·d(CATTATAC). Using starting structures from different locations in conformational space (e.g. A-DNA and B-DNA), the rMC calculations readily converged, with a root-mean-square deviation (RMSD) of <0.3 Å between structures generated using different protocols and starting structures. Theoretical 2D NOE peak intensities were calculated for the rMC-generated structures using the complete relaxation matrix program CORMA, enabling a comparison with experimental intensities via residual indices. Simulation of the vicinal proton coupling constants was carried out for the structures generated, enabling a comparison with the experimental deoxyribose ring coupling constants, which were not utilized in the structure determination in the case of the rMC simulations. Agreement with experimental 2D NOE and scalar coupling data was good in all cases. The rMC structures are quite similar to that refined by a traditional restrained MD approach (RMSD<0.5 Å) despite the different force fields used and despite the fact that MD refinement was conducted with additional restraints imposed on the endocyclic torsion angles of deoxyriboses. The computational time required for the rMC and rMD calculations is about the same. A comparison of structural parameters is made and some limitations of both methods are discussed with regard to the average nature of the experimental restraints used in the refinement.Abbreviations MC Monte Carlo - rMC restrained Monte Carlo - MD molecular dynamics - rMD restrained molecular dynamics - DG distance geometry - EM energy minimization - 2D NOE two-dimensional nuclear Overhauser effect - DQF-COSY double-quantum-filtered correlation spectroscopy - RMSD root-mean-square deviation To whom correspondence should be addressed.     

An estimate of spin diffusion in a spin subset: Application to iterative distance calculation from 3D 15N NOESY-HMQC

Summary A method for quantification of distances between amide hydrogens using only the 3D NOESY-HMQC experiment recorded on a ¹⁵N-labelled protein is presented. This method is based on an approximate expression of the NOE intensities between amide hydrogens obtained from continuum modelling of the non-amide spins; this expression is used in a distance calculation algorithm. The algorithm has been named CROWD, standing for Continuum approximation of Relaxati On path Ways between Dilute spins. This approximation as well as the CROWD algorithm are tested on a simulated case; the CROWD algorithm is then applied to experimental data, measured on a fragment of bacteriorhodopsin.     

Measurement of carbonyl chemical shifts of excited protein states by relaxation dispersion NMR spectroscopy: comparison between uniformly and selectively 13C labeled samples

Carr-Purcell-Meiboom-Gill (CPMG) relaxation dispersion nuclear magnetic resonance (NMR) spectroscopy has emerged as a powerful method for quantifying chemical shifts of excited protein states. For many applications of the technique that involve the measurement of relaxation rates of carbon magnetization it is necessary to prepare samples with isolated (13)C spins so that experiments do not suffer from magnetization transfer between coupled carbon spins that would otherwise occur during the CPMG pulse train. In the case of (13)CO experiments however the large separation between (13)CO and (13)C(alpha) chemical shifts offers hope that robust (13)CO dispersion profiles can be recorded on uniformly (13)C labeled samples, leading to the extraction of accurate (13)CO chemical shifts of the invisible, excited state. Here we compare such chemical shifts recorded on samples that are selectively labeled, prepared using [1-(13)C]-pyruvate and NaH(13)CO(3,) or uniformly labeled, generated from (13)C-glucose. Very similar (13)CO chemical shifts are obtained from analysis of CPMG experiments recorded on both samples, and comparison with chemical shifts measured using a second approach establishes that the shifts measured from relaxation dispersion are very accurate.     

NMR spectroscopy for studying structure and intramolecular dynamics of modified analogs of steroid hormones

Special features of the use of homo- and heteronuclear correlation methods of NMR in one and two dimensions for studying the spatial structure and intramolecular dynamics of modified analogues of steroid hormones (MASH) are considered. The application of these methods to the assignment of resonances in the high-field 1H NMR region and to the determination of the most stereospecifically important parameters, such as the vicinal constants of spin-spin coupling (3JH-H) and nuclear Overhauser effects (NOE), are discussed using the example of NMR studies of some estrogens and androgens at 300 MHz and on the basis of literature data. The most efficient combination of the methods and the necessary modification of each of them may be chosen considering the spectral and relaxation parameters of MASH in liquid medium, including the anisotropy of the overall diffusive motion. The characteristics of MASH are the wide use of correlations through long-range couplings (COSY-45 and DQF-COSY), the application of the 4,5JH-H constants for the determination of spatial structure, and the advantage of heteronuclear HSQC methods with and without 13C decoupling over the corresponding HMQC methods in both resolution and sensitivity. In the conformationally rigid MASH molecules, the anisotropy of the MASH diffusive motion in liquid adversely affects the determination of interproton distances by the calibrating processing method for the NOE difference and NOESY spectra: it results in both overestimated and underestimated distance values depending on the polar angle ratios of the reference and the determined distances. Under certain conditions, conformationally mobile MASH demonstrate the additional contribution of the scalar relaxation mechanism between the indirectly (scalarly) bound protons. This mechanism is responsible for the underestimated values of NOE and the corresponding errors in the distance determination.     

Accuracy of bound peptide structures determined by exchange transferred nuclear Overhauser data: A simulation study

The exchange-transferred NOE method to determine the three-dimensional structure of peptides bound to proteins, or other macromolecular systems, is becoming increasingly important in drug design efforts and for large or multicomponent assemblies, such as membrane receptors, where structural analysis of the full system is intractable. The exchange-transferred nuclear Overhauser effect spectroscopy (etNOESY) method allows the determination of the bound-state conformation of the peptide from the intra-molecular NOE interactions between ligand protons. Because only ligand–ligand NOEs are generally observable, the etNOESY method is restricted to fewer NOEs per residue than direct protein structure determination. In addition, the averaging of relaxation rates between free and bound states affects the measured cross-peak intensities, and possibly the accuracy of distance estimates. Accordingly, the study reported here was conducted to examine the conditions required to define a reliable structure. The program CORONA was used to simulate etNOE data using a rate-matrix including magnetic relaxation and exchange rates for two peptide–protein complexes derived from the reference complex of cAMP-dependent protein kinase ligated with a 24-residue inhibitor peptide. The results indicate that reasonably accurate peptide structures can be determined with relatively few NOE interactions when the interactions occur between non-neighboring residues. The reliability of the structural result is suggested from the pattern of NOE interactions. A structure with an accuracy of approximately 1.3 Å rms difference for the main-chain atoms can be obtained when etNOE interactions between non-neighboring residues occur over the length of the peptide. The global precision is higher (approximately 0.9 Å rms difference) but is not correlated to global accuracy. A local definition of precision along the backbone appears to be a good indicator of the local accuracy.     

A variable target intensity-restrained global optimization (VARTIGO) procedure for determining three-dimensional structures of polypeptides from NOESY data: Application to gramicidin-S

Summary A global optimization method for intensity-restrained structure refinement, based on variable target function (VTF) analysis, is illustrated using experimental data on a model peptide, gramicidin-S (GS) dissolved in DMSO. The method (referred to as VARTIGO for variable target intensity-restrained global optimization) involves minimization of a target function in which the range of NOE contacts is gradually increased in successive cycles of optimization in dihedral angle space. Several different starting conformations (including all-trans) have been tested to establish the validity of the method. Not all optimizations were successful, but these were readily identifiable from their large NOE R-factors. We also show that it is possible to simultaneously optimize the rotational correlation time along with the dihedral angles. The structural features of GS thus obtained from the successful optimizations are in excellent agreement with the available experimental data. A comparison is made with structures generated from an intensity-restrained single target function (STF) analysis. The results on GS suggest that VARTIGO refinement is capable of yielding better quality structures. Our work also underscores the need for a simultaneous analysis of different NOE R-factors in judging the quality of optimized structures. The NOESY data on GS in DMSO appear to provide evidence for the presence of two orientations for the ornithine side chain, in fast exchange. The NOESY spectra for this case were analyzed using a relaxation rate matrix which is a weighted average of the relaxation rate matrices for the individual conformations.     

A 31P-NMR spin-lattice relaxation and 31P[1H] nuclear Overhauser effect study of sonicated small unilamellar phosphatidylcholine vesicles.

The motional properties of the inner and outer monolayer headgroups of egg phosphatidylcholine (PC) small unilamellar vesicles (SUV) were investigated by 31P-NMR temperature-dependent spin-lattice relaxation time constant (T1) and 31P[1H] nuclear Overhauser effect (NOE) analyses. Three different aspects of the dynamics of PC headgroups were investigated using the T1 analysis. First, differences in the dynamics of the headgroup region of both surfaces of the SUV were measured after application of a chemical shift reagent, PrCl3, to either the extra- or intravesicular volumes. Second, the ability of the T1 experiment to resolve the different motional states was evaluated in the absence of shift reagent. Third, comparison between correlation times obtained from a resonance frequency dependent 31P[1H] NOE analysis allowed a determination of the applicability of a simplified motional model to describe phosphorus dipolar relaxation. Temperature-dependent 31P-NMR T1 values obtained for the individual monolayers at 81.0 and 162.0 MHz were modelled assuming that phosphorus undergoes both a dipolar and an anisotropic chemical shielding relaxation mechanism, each being described by the same correlation time, tau. At 162.0 MHz, the position of the T1 minimum for the inner monolayer was 9 degrees higher than that of the outer region, indicating a higher level of motional restriction for the inner leaflet, in agreement with 31P[1H] NOE measurements. The 162.0 MHz T1 profile of the combined SUV monolayers exhibited a smooth minimum located at the midpoint of the monolayer minima positions, effectively masking the presence of the individual surfaces. 31P[1H] NOE results obtained at 32.3, 81.0 and 162.0 MHz did not agree with those predicted from a simple dipolar relaxation model. These results suggest a T1-temperature method can neither discriminate two or more closely related motional time scales in a heterogeneous environment (such as incorporation of protein into lipid bilayers) nor allow accurate determination of the correlation time at the position of the minimum when the dipolar relaxation rate makes a significant contribution to the overall rate.     

High resolution nuclear magnetic resonance studies of nigeran

Polymer motion in solution can be studied by ¹³CNMR relaxation methods, which provide information about the correlation time for C-H vectors. ¹³C-Relaxation and Nuclear Overhauser Enhancement (NOE) data may frequently be combined to determine the dipole-dipole relaxation contribution. An alternative method is proposed based on a comparison of the proton spin-lattice relaxation rates of the centre proton resonances of an unlabelled molecule with the relaxation rates of the ¹³C satellites (from ¹³C labelled molecules).Selectively labelled nigeran which is an alternating $\text{1 → 3 and 1 → 4 α-}\text{d}\text{-glucan}$ has been investigated. The discussion in terms of the occurrence of different motions for each of the two units of the polymer requires an unambiguous assignment of the two anomeric carbons. For this reason a detailed assignment of the ¹H and ¹³C Nuclear Magnetic Resonance (NMR) spectra of nigeran in dimethylsulphoxide-d₆ is described, based on T₁ and NOE measurements in addition to selective homonuclear and heteronuclear spin decoupling experiments. These values are correlated with a conformation estimated by HSEA hard-spheres calculation. The measurements of the relaxation parameters for labelled and unlabelled compounds which provide an alternative determination of the ¹³C-¹H dipole-dipole relaxation contribution in a macromolecule agree well with ¹³C-{¹H} NOE experiments.     

Identification and removal of nitroxide spin label contaminant: impact on PRE studies of α-helical membrane proteins in detergent

NMR paramagnetic relaxation enhancement (PRE) provides long‐range distance constraints (～15–25 Å) that can be critical to determining overall protein topology, especially where long‐range NOE information is unavailable such as in the case of larger proteins that require deuteration. However, several challenges currently limit the use of NMR PRE for α‐helical membrane proteins. One challenge is the nonspecific association of the nitroxide spin label to the protein‐detergent complex that can result in spurious PRE derived distance restraints. The effect of the nitroxide spin label contaminant is evaluated and quantified and a robust method for the removal of the contaminant is provided to advance the application of PRE restraints to membrane protein NMR structure determination.     

A complete algorithm to resolve ambiguity for intersubunit NOE assignment in structure determination of symmetric homo-oligomers

Assignment of nuclear Overhauser effect (NOE) data is a key bottleneck in structure determination by NMR. NOE assignment resolves the ambiguity as to which pair of protons generated the observed NOE peaks, and thus should be restrained in structure determination. In the case of intersubunit NOEs in symmetric homo-oligomers, the ambiguity includes both the identities of the protons within a subunit, and the identities of the subunits to which they belong. This paper develops an algorithm for simultaneous intersubunit NOE assignment and C(n) symmetric homo-oligomeric structure determinations, given the subunit structure. By using a configuration space framework, our algorithm guarantees completeness, in that it identifies structures representing, to within a user-defined similarity level, every structure consistent with the available data (ambiguous or not). However, while our approach is complete in considering all conformations and assignments, it avoids explicit enumeration of the exponential number of combinations of possible assignments. Our algorithm can draw two types of conclusions not possible under previous methods: (1) that different assignments for an NOE would lead to different structural classes, or (2) that it is not necessary to uniquely assign an NOE, since it would have little impact on structural precision. We demonstrate on two test proteins that our method reduces the average number of possible assignments per NOE by a factor of 2.6 for MinE and 4.2 for CCMP. It results in high structural precision, reducing the average variance in atomic positions by factors of 1.5 and 3.6, respectively.     

Accurate estimation of inter-atomic distances in large proteins by NMR.

Recently a method was proposed which permits the extraction of the exact interatomic distance information from the measurement of the evolution of a single cross-peak relative to the mixing time in a NOESY experiment. This is performed through a careful multi-exponential analysis allowing the extraction of the relaxation parameter, and, consequently, the inter-proton distance. We investigate in the present paper whether this technique, already evaluated theoretically, can be used in a real experimental case. We have recorded and analyzed a set of 56 NOESY experiments on a lysozyme sample. Some 81 nOe build-up curves obtained from these data were analyzed in terms of distance. It is shown that the correlation between the measured distances and the reference distances obtained from crystallographic studies, is quite good. An accuracy of the order of 10% is obtained.     

Determination of dihedral Psi angles in large proteins by combining NH(N)/C(alpha)H(alpha) dipole/dipole cross-correlation and chemical shifts

We propose a strategy based on the combination of experimental NH(N)/C(alpha)H(alpha) dipole/dipole cross-correlated relaxation rates and chemical shift analysis for the determination of Psi torsion angles in proteins. The method allows the determination of a dihedral angle that is not easily accessible by nuclear magnetic resonance (NMR). The measurement of dihedral angle restraints can be used for structure calculation, which is known to improve the quality of NMR structures. The method is of particular interest in the case of large proteins, for which spectral assignment of the nuclear Overhauser effect spectra, and therefore straightforward structural determination, is out of reach. One advantage of the method is that it is reasonably simple to implement, and could be used in association with other methods aiming at obtaining structural information on complex systems, such as residual dipolar coupling measurements. An illustrative example is analyzed in the case of the 30-kDa protein 6-phosphogluconolactonase.     

Intermolecular relaxation has little effect on intra-peptide exchange-transferred NOE intensities

Exchange-transferred nuclear Overhauser enhancement (etNOE) provides a useful method for determining the 3-dimensional structure of a ligand bound to a high-molecular-weight complex. Some concern about the accuracy of such structures has arisen because indirect relaxation can occur between the ligand and macromolecule. Such indirect relaxation, or spin diffusion, would lead to errors in interproton distances used as restraints in structure determination. We address this concern by assessing the extent of intermolecular spin diffusion in nineteen peptide-protein complexes of known structure. Transferred NOE intensities were simulated with the program CORONA (Calculated OR Observed NOESY Analysis) using the rate-matrix approach to include contributions from indirect relaxation between protein-ligand and intraligand proton pairs. Intermolecular spin diffusion contributions were determined by comparing intensities calculated with protonated protein to those calculated with fully deuterated protein. The differences were found to be insignificant overall, and to diminish at short mixing times and high mole ratios of peptide to protein. Spin diffusion between the peptide ligand and the protein contributes less to the etNOE intensities and alters fewer cross peaks than the well-studied intramolecular spin diffusion effects. Errors in intraligand interproton distances due to intermolecular relaxation effects were small on average and can be accounted for with the restraint functions commonly used in NMR structure determination methods. In addition, a rate-matrix approach to calculate distances from etNOESY intensities using a volume matrix comprising only intraligand intensities was found to give accurate values. Based on these results, we conclude that structures determined from etNOESY data are no less accurate due to spin diffusion than structures determined from conventional NOE intensities.     

A calculation strategy for the structure determination of symmetric demers by 1H NMR

The structure determination of symmetric dimers by NMR is impeded by the ambiguity of inter- and intramonomer NOE crosspeaks. In this paper, a calculation strategy is presented that allows the calculation of dimer structures without resolving ther ambuguity by additional experiments (like asymmetric labeling). The strategy employs a molecular dynamic-based simulated annealing approach to minimize a traget function. The experimental part of the target function contains distance restraints that correctly describe the ambiguity of the NOE peaks, and a novel term that restrains the symmetry of the dimer without requiring the knowledge of the symmetry axis. The use of the method is illustrated by three examples, using experimentally obtained data and model data derived from a known structure. For the purpose of testing the method, it is assumed that every NOE crosspeak is ambiguous in all three cases. It is shown that the structure of a homologous protein is known and in ab intio structure determination. The method can be extended to higher order symmetric multimers. © 1993 Wiley-Liss, Inc.     

Solvent interactions with the Trp-cage peptide in 35% ethanol-water

Intermolecular NOE experiments have been used to explore interactions of water and ethanol molecules in 35% ethanol/65% water (v/v) with the peptide Trp-cage at temperatures from 5 to 25 degrees C. Magnetic dipole-dipole cross-relaxation terms sigma(HH) (NOE) and sigma(HH) (ROE) for interaction of solvent components with spins of the peptide suggest that ethanol molecules associate with backbone atoms for times of the order of nanoseconds at 5 degrees C. Formation of peptide-ethanol complexes can also account for the larger-than-expected values of cross-relaxation terms at higher temperatures. Hydrocarbon side chains of the peptide do not appear to experience such interactions with ethanol. Cross relaxation resulting from water-peptide interactions are consistent with long-lived water interactions with the backbone atoms. Water cross relaxation with nonpolar side chains of the peptide (Leu2, Ile4, Leu7, and proline residues) are only those expected for bulk solvent. However, long-lived association of both water and ethanol with the polar side chains of Tyr3 and Trp6 is indicated by the data. (c) 2008 Wiley Periodicals, Inc. Biopolymers 89: 862-872, 2008.This article was originally published online as an accepted preprint. The "Published Online" date corresponds to the preprint version. You can request a copy of the preprint by emailing the Biopolymers editorial office at biopolymers@wiley.com.     

A transferred NOE study of a tricyclic analog of acyclovir bound to thymidine kinase

Summary A purine derivative with an acyclic sugar analog, 3,9-dihydro-3-[(2-hydroxyethoxy)methyl]-6-ethyl-9-oxo-5H-imidazo[1,2-a]purine, was studied in the free state and in complex with herpes simplex virus thymidine kinase (HSV1 TK). Transferred NOE experiments, combined with a full relaxation matrix analysis of the substrate's spin system, resulted in a set of distance constraints for all proton pairs. These constraints were used in structure determination procedures based on simulated annealing and molecular dynamics simulations to obtain a family of structures compatible with the experimental NMR data. The results indicate that, although in both states the chains have the syn orientation with respect to the aromatic rings, in the free state the substrate's acyclic moiety is relatively disordered, while in the bound state only one specific conformation is preferred. Fluctuations can only be seen in the case of the terminal hydroxyl group, for which no NOE was recorded and hence no constraints were available.     

Relaxation data in NMR structure determination: model calculations for the lysozyme-Gd3+ complex

The effect of including paramagnetic relaxation data as additional restraints in the determination of protein tertiary structures from NMR data has been explored by a systematic series of model calculations. The system used for testing the method was the 2.0 A resolution tetragonal crystal structure of hen egg white lysozyme (129 amino acid residues) and structures were generated using a version of the hybrid "distance geometry-dynamic simulated annealing" procedure. A limited set of 769 NOEs was used as restraints in all the calculations; the strengths of these were categorized into three classes on the basis of distances observed in the crystal structure. The values of 50 phi angles were also restrained on the basis of amide-alpha coupling constants calculated from the X-ray structure. Five sets of 12 structures were determined using differing sets of paramagnetic relaxation data as restraints additional to those involving the NOE and coupling constant data. The paramagnetic relaxation data were modeled on the basis of the distances of defined protons from the crystallographic binding site of Gd3+ in lysozyme. Analysis of the results showed that the relaxation data significantly improved the correspondence between the set of generated structures and the crystal structure, and that the more well defined the relaxation data, the more significant the improvement in the quality of the structures. The results suggest that the inclusion of paramagnetic relaxation restraints could be of significant value for the experimental determination of protein structures from NMR data.